2. In a large bowl, mix together water, lemon juice, sugar, and salt until dissolved. Add lemon quarters and chicken. Marinate 30 minutes.

3. Remove chicken from marinade and pat dry. Preheat a grill pan over medium heat. Massage 1 drop liquid smoke into each chicken breast. Salt and pepper generously, then rub 1 tablespoon butter over and under skin of each chicken breast, placing 2 sage leaves underneath skin. Place on hot grill pan, skin side down, until skin is golden brown, about 5 minutes. Transfer chicken to a baking sheet and bake until cooked through, about 25 minutes.

4. Meanwhile, in a large sauté pan over medium heat, melt 2 tablespoons butter with olive oil. Add onion, mushrooms, and cayenne pepper. Sauté until onions are translucent and mushrooms are tender, about 8 minutes. Add wine and reduce until almost evaporated. Add chicken stock and simmer until reduced by 1/3.

5. In a small bowl press together remaining butter and flour with fingertips until well blended, then slowly add to sauce while stirring with a wooden spoon. Simmer until sauce resembles loose gravy, about 5 minutes. Serve warm with chicken.